Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits

Learn about efficient methods for understanding linear properties of quantum circuits through this 18-minute conference talk from QTML 2025. Explore the fundamental challenge of capturing dynamics in modern quantum computers where the vast many-qubit state space prevents comprehensive classical simulations or quantum tomography. Discover how researchers address the critical question of whether linear properties of many-qubit circuits with tunable RZ gates and Clifford gates can be efficiently learned from measurement data by varying classical inputs. Examine the proven requirement that sample complexity must scale linearly while computational complexity may scale exponentially, and understand the proposed kernel-based solution using classical shadows and truncated trigonometric expansions that enables controllable trade-offs between prediction accuracy and computational overhead. Gain insights into applications across quantum information processing protocols, Hamiltonian simulation, and variational quantum algorithms validated through numerical simulations on systems up to 60 qubits, advancing both practical quantum algorithm exploration and learning-based quantum system certification.